Analysis of Fluid-Structure Interactions using Information Theory

The challenges of analyzing interactions between stochastic structures in a fluid can be ameliorated by recasting the problem as a system of information transfer.  Information flow can be resolved from the time series of structure displacement or the fluid velocity, thereby circumventing the need to resolve the fluid interactions between the structures. Transfer Entropy (TE) provides a model-free method for analyzing interactions of fluid-structure interactions. The TE function is a non-symmetric measure of the reduction in uncertainty in the state of one variable due to knowledge about the state of another. Here it is employed to measure the directional Granger Causality between two structures, map the extent of fluid influenced by the structures and quantify the time lags associated with the various communication paths. The experiment consisted of a stochastically rotating cylinder, driven by a first order Markov system, with a passively pivoted airfoil located directly downstream. Laser Doppler Velocimetry (LDV) was used to measure the local fluid velocity at various points upstream of the airfoil and optical tracking was used to obtain the structure displacements. The causality of this simple system is known a priori, allowing for validation of the proposed method.